Position Vectors Distance between 2 points

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Presentation transcript:

Position Vectors Distance between 2 points

2D Position Vectors - 1 The displacement of an object from the origin is called it’s Position Vector R O r OR Every point has a unique position vector

2D Position Vectors - 2 R A position vector is r fixed to the origin O A free vector has magnitude and direction, but is not fixed to the origin s

r + s = t s = t - r Position Vectors – example 1 R r O s t T What is the displacement from R to T? r + s = t O s = t - r t T

A a = xi + yj + zk 3D Position Vectors z a y o x Similarly in 3D, all points have position vectors a y e.g. The position vector of point A o a = xi + yj + zk x

a + = b = b - a Distance between 2 points B A |AB| = (52 + 52 + 82) z A and B have position vectors x y z b B What is the distance between them? AB a A a + = b AB AB = b - a |AB| = (52 + 52 + 82) = 114 = 10.7 AB

= b - a Distance between 2 points - general case B A A and B have position vectors x y z B b What is the distance between them? A a AB = b - a AB |AB| = (x2-x1)2 + (y2-y1)2 + (z2-z1)2